So I just added /page/1 to the searchform code, so now it reads:
action="<?php bloginfo('url'); ?>/page/1"

And it works! Good enough for me. But I still have no idea what caused the problem in the first place. My best guess at that when she refers to the Dragon Con convention as D*C, somewhere that asterisk broke something. Though I tried adding asterisks to different letters in the title, body and tags, I was unable to break another letter and repeat the original problem. But hey, at least searching works.